A race is measured to have a distance of 10.6 km, correct to the nearest 0.1 km - Edexcel - GCSE Maths - Question 23 - 2022 - Paper 2

Sam runs the race in 31 minutes and 48 seconds. To convert this into hours:

1. Convert minutes to hours: 31 ext{ minutes} = rac{31}{60} ext{ hours}

2. Convert seconds to hours: 48 ext{ seconds} = rac{48}{3600} ext{ hours}

Adding these gives:

t = rac{31}{60} + rac{48}{3600} = rac{1860 + 48}{3600} = rac{1908}{3600} ext{ hours}

Calculating gives:

$t hickapprox 0.529 ext{ hours}$

The average speed $v$ is calculated using the formula:

v = rac{d}{t}

Using upper and lower bounds for distance:

1. For the upper bound: v_{UB} = rac{10.65 ext{ km}}{0.529 ext{ hours}} hickapprox 20.16 ext{ km/h}

2. For the lower bound: v_{LB} = rac{10.55 ext{ km}}{0.529 ext{ hours}} hickapprox 19.98 ext{ km/h}

The average speed, calculated from both bounds, lies between:

$19.98 ext{ km/h} < v < 20.16 ext{ km/h}$

Since the average speed varies less than 0.2 km/h, we can round this to one decimal place:

Thus, a suitable value for $v$ is:

$v hickapprox 20.1 ext{ km/h}$